For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to N decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty.
However, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits. Beware that roundoff errors can accumulate. If M decimal places are used in the intermediate calculation, we say there are M-N guard digits.
References
Forman S. Acton. Numerical Methods that Work, The Mathematical Association of America (August 1997).
